scholarly journals GAMANL: A COMPUTER PROGRAM APPLYING FOURIER TRANSFORMS TO THE ANALYSIS OF GAMMA SPECTRAL DATA.

1968 ◽  
Author(s):  
T Harper ◽  
T Inouye ◽  
N Rasmussen
Keyword(s):  
Computer Program ◽  
Spectral Data ◽  
Fourier Transforms

scholarly journals Coefficient-of-Determination Discrete Fourier Transform

2018 ◽  
Author(s):  
Matthew Marko
Keyword(s):  
Spectral Data ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Coefficient Of Determination ◽  
Temporal Data ◽  
Discrete Fourier Transforms ◽  
Time Domain Data ◽  
Sinusoidal Functions ◽  
The Time Domain

This algorithm is designed to perform Discrete Fourier Transforms (DFT) to convert temporal data into spectral data. This algorithm obtains the Fourier Transforms by studying the Coefficient of Determination of a series of artificial sinusoidal functions with the temporal data, and normalizing the variance data into a high-resolution spectral representation of the time-domain data with a finite sampling rate. What is especially beneficial about this DFT algorithm is that it can produce spectral data at any user-defined resolution.

scholarly journals Discrete Spherical Harmonic Transforms for Equiangular Grids of Spatial and Spectral Data

2011 ◽  
Vol 1 (1) ◽  
pp. 9-16 ◽  
Author(s):  
J. Blais
Keyword(s):  
Fourier Transform ◽  
Spectral Data ◽  
Spherical Harmonic ◽  
Fourier Transforms ◽  
Data Matrix ◽  
Geopotential Model ◽  
Double Precision ◽  
Analysis And Synthesis ◽  
Double Precision Arithmetic ◽  
Band Limited

Discrete Spherical Harmonic Transforms for Equiangular Grids of Spatial and Spectral DataSpherical Harmonic Transforms (SHTs) which are non-commutative Fourier transforms on the sphere are critical in global geopotential and related applications. Among the best known global strategies for discrete SHTs of band-limited spherical functions are Chebychev quadratures and least squares for equiangular grids. With proper numerical preconditioning, independent of latitude, reliable analysis and synthesis results for degrees and orders over 3800 in double precision arithmetic have been achieved and explicitly demonstrated using white noise simulations. The SHT synthesis and analysis can easily be modified for the ordinary Fourier transform of the data matrix and the mathematical situation is illustrated in a new functional diagram. Numerical analysis has shown very little differences in the numerical conditioning and computational efforts required when working with the two-dimensional (2D) Fourier transform of the data matrix. This can be interpreted as the spectral form of the discrete SHT which can be useful in multiresolution and other applications. Numerical results corresponding to the latest Earth Geopotential Model EGM 2008 of maximum degree and order 2190 are included with some discussion of the implications when working with such spectral sequences of fast decreasing magnitude.

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